Statistical Link between External Climate Forcings and Modes of Ocean Variability

Abdul Malik^{1, 2}, Stefan Brönnimann^{1, 2}, Paolo Perona³

1. Introduction

The driving factors of AMO are unclear and currently a focus of research. Inter-annual to multidecadal scale Sea Surface Temperature (SST) variations exist in the Atlantic Ocean (Otterå et al. 2010) where AMO exhibits itself as a prominent multidecadal scale (55-80 years) oscillation between warm and cold phases of SSTs (Knight et al. 2006; Wei et al. 2012). Recent studies using reconstruction dataset (see, Knudsen et al. 2014) and climate model simulations (see, Stenchikov et al. 2009; Otterå et al. 2010) indicate that external forcing factors i.e. solar activity and volcanic eruptions can drive the AMO. Knudsen et al. 2014 and Otterå et al. 2010 showed that after termination of the Little Ice Age (LIA) the combined solar and volcanic forcing leads the AMO by ~5 years. Jiang et al. (2015) using proxy reconstruction dataset showed that SSTs in the northern North Atlantic are linked with solar activity in the past 4000 years. Booth et al. (2012) using an Earth system climate model showed that anthropogenic aerosols and volcanic activity can explain 76% multi-decadal variance of north Atlantic SSTs over the period AD 1860-2005. Can a coupled Atmosphere-Ocean-Chemistry climate model simulate the relationship between external forcings and AMO as found by the previous studies?

Observational and climate model based studies suggest the influence of external climate forcings on ENSO on inter-annual and multidecadal timescales. In general, studies show a negative correlation between ENSO and solar activity on inter-annual and multidecadal timescales (e.g., Mehta et. al. 1997; Kodera 2005; Mann et al. 2005; Meehl et. al. 2009; Narashimha et. al. 2010). In contrast to these studies, on multidecadal timescale, Fan et al. (2009) using climate model simulations found a positive correlation between solar activity and Niño3 index which indicate uncertainty in their relationship. The proxy based studies (e.g., Adams et al. 2003) show an El-Niño like pattern in equatorial Pacific Ocean after volcanic eruptions. However, the response of equatorial Pacific SSTs to volcanic eruption is not consistent among climate models as some simulate an El-Niño like response (e.g., Ohba et al. 2013; Maher et al. 2015; Pausata et al. 2015) whereas others show a La-Niña like response (e.g. McGregor et al. 2011; Zanchettin et al. 2012). The contradicting findings of Fan et al. (2009), McGregor et al. (2011), and Zanchettin et al. (2012) compared to other studies indicate that the response of ENSO to external forcings is inconsistent among climate models and needs to be further investigated.

The North Pacific SSTs also have two distinct modes of variability i.e. inter-annual and decadal (Yeh et al. 2003). The decadal mode, PDO, is the leading principal component of SSTs in the north Pacific with periodicities 15-25 years and 50-70 years (e.g., Mantua et al. 2002). The inter-annual mode of north Pacific SSTs simultaneously correlates with tropical Pacific inter-annual SST variability whereas the decadal mode leads the tropical Pacific decadal SST variability by 5~7 years (Yeh et al. 2003). Newman et al. (2003, 2016) found that PDO depends on ENSO on all timescales. There are several other studies which indicate interaction between the PDO and ENSO (e.g., Zhang et al. 1996; Barnett et al. 1999; Pierce et al. 2000; Fedorov et al. 2000, 2001; Vimont et al. 2001, 2003a, b; Schneider et al. 2005; Newman 2007). Similarly, there are studies which show a link of AMO with PDO (see, D’Orgeville et al. 2007; Zhang et al. 2007; Wu et al. 2011; Kucharski et al. 2015) and ENSO (see, Dong et al. 2002, 2006, 2007; Timmermann et al. 2005, 2007; Goswami et al. 2006; Sutton et al. 2007; Kucharski et al. 2011; Frauen et al. 2012; Kang et al. 2014; Kayano et al. 2014; McGregor et al. 2014). It should be investigated whether a complex interaction between modes of ocean variability affects their relationship, if exists, with external forcings.

In the present work we investigate the statistical link between modes of ocean variability and external climate forcings using De-trended Semi-partial Cross-Correlation Analysis (DSPCCA). Recently Yuan et al. (2015) developed De-trended Partial-Cross-Correlation Analysis (DPCCA) technique to analyse correlation between two time series which are correlated to other signals as well. We extend DPCCA to DSPCCA using the method proposed by Kim (2015). The DPCCA is a combination of two statistical techniques i.e. De-trended Cross-Correlation Analysis (DCCA), and Partial-Cross-Correlation Analysis (PCCA). The DPCCA can analyse a complex system of several interlinked variables. Often, climatic variables subjected to cross correlation are simultaneously tele-connected with several other variables and it is not easy to isolate their intrinsic/direct relationship. In the presence of non-stationarities and periodic background signals the calculated correlation coefficients can be overestimated or inaccurate (Yuan et al. 2015). The DCCA has the advantage over traditional correlation analysis that it accurately measures the correlation coefficient between two variables even if any level of non-stationarity (or local trend) is present (Kristoufek 2015). Another advantage of the DCCA is that it can be used to study the relationship between two variables on different time scales (Dong et. al. 2014). The DPCCA method removes the non-stationarities (using DCCA) as well as partials out the influence of background signals (using PCCA) from the variables being cross correlated and thus gives a robust estimate of correlation.

In a complex scenario where AMO, PDO, and ENSO have simultaneous/lead/lagged interactions with each other on different timescales, and where external forcings also play their role, it urges to investigate the intrinsic (true) relationship between the ocean modes of variability and external climate forcings. Can the factors, for instance the PDO and ENSO, modulate the strength of the relationship between the AMO and external forcings on different timescales? We investigate the extrinsic (in the presence of potential modulating factors) as well as the intrinsic (in the absence of potential modulating factors) correlation between modes of ocean variability (AMO, PDO, and Niño3) and external forcings (solar activity and volcanic eruptions) on inter-annual (3-yr) to centennial (100-yr) timescales. We employ DCCA, and DSPCCA techniques on observational (AD 1854-1999) and proxy (AD 1600-1999) datasets, and coupled Atmosphere-Ocean-Chemistry (AOCCM) climate model simulations with SOCOL MPIOM to answer following questions: (1) is there any link between modes of ocean variability and external forcings (2) at what timescales these modes of ocean variability are linked to external forcings and (3) can the complex interaction among the ocean modes of variability modulate their relationship with external forcings?

The paper is organized as follows. Section 2 presents the data and methods. The results are demonstrated in section 3. Finally, the discussion and conclusions are summarized in section 4.

2. Data and Methods

2.1. Model Description
A coupled atmosphere-ocean-chemistry climate model is important to reasonably simulate the influence of solar activity and volcanic eruptions on atmosphere and ocean (see, Kodera 2004, 2005; Meehl et al. 2009; Reichler et al. 2012). Therefore, the present study employs four transient simulations (i.e., L1, L2, M1, and M2) carried out with the coupled Atmosphere-Ocean-Chemistry Climate Model (AOCCM) SOCOL-MPIOM over the period AD 1600-1999 with all major forcings. The model has a horizontal grid of T31 (≈3.75^o×3.75^o) with 39 irregular vertical pressure levels (L39) up to 0.01 hPa. The ocean component (MPIOM) of the model has horizontal resolution of 3^o which varies between 22 km (Greenland) and 350 km (Tropical Pacific). The model was nudged to QBO reconstruction according to Brönnimann et al. (2007). All four simulations were run with different ocean initial condition. The model was forced with TSI reconstruction of Shapiro et al. (2011) which is considerably different in terms of amplitude from the other TSI reconstructions (e.g., Lean et al. 1995; Krivova et al. 2011). The simulations L1 and L2 were carried out with strong irradiance amplitude (6 W/m²) of 1 W/m² forcing, whereas M1 and M2 were carried out with medium irradiance amplitude (3 W/m²) of 0.5 W/m² forcing. The calculation time step for dynamical processes is 15 minutes and 144 minutes for the ocean component. The atmosphere-ocean coupling takes place every 24 hours (Anet et al. 2013a, b; Muthers et al. 2014).

2.2. Datasets

2.2.1. Gridded SST datasets
Two gridded SST reconstructions, in addition to the model output, i.e. the Extended Reconstructed Sea Surface Temperature version 4 (ERSSTv4) (Liu et al. 2014; Huang et al. 2015, 2016) over the period AD 1854-1999, and SST reconstruction by Mann et al. (2009) over the period AD 1600-1999 (hereafter, Mann-Recon) are used in the present study. The ERSSTv4 has global coverage with a horizontal resolution of 2^o×2^o. The ERSSTv4 data is provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA (http://www.esrl.noaa.gov/psd/). Mann-Recon is a multiproxy reconstruction based on more than a thousand tree rings, ice cores, corals, sediments, and other proxies. The Mann-Recon does not show inter-annual variability and is meaningful only at inter-decadal to longer timescales (Mann et al. 2009). Therefore, we use a slightly modified version of this reconstruction by Bhend et al. (2012) (hereafter, Mann-ReconMod). The Mann-Recon was inter- and extra-polated to T63 (approximately 1.85^o×1.85^o) and then superimposed with a seasonal cycle and ENSO-dependent intra-annual variability. The seasonal cycle was derived from HadISST1.1 of Rayner et al. (2003) and ENSO-dependent intra-annual variability was obtained by regressing Niño3.4 index of Cook et al. (2008) onto HadISST1.1 (Bhend J, personal communication, 2015).

2.2.2. AMO Index

We also use AMO reconstruction by Gray et al. (2004) over the period AD 1600-1990 (hereafter, AMO-Gray) downloaded from the web site of NOAA National Centers for Environmental Information (NCEI; http://www.ncdc.noaa.gov/data-access/paleoclimatology-data/datasets/tree-ring). The AMO-Gray is based on tree-ring chronologies from eastern North America, Europe, Scandinavia, North Africa, and the Middle East (Gray et al. 2004). The AMO reconstruction by Mann et al (2009) and Gray et al. (2004) are the best amongst the available historical AMO reconstructions (Knudsen et al. 2014). All the AMO indices used in this study are shown in Fig. 1a.

2.2.3. PDO Index
The PDO index based on ERSSTv4 over the period AD 1854-1999 is downloaded from the web site of NCEI (hereafter PDO-ERSST; http://www.ncdc.noaa.gov/teleconnections/pdo/). For Mann-ReconMod, and model, the PDO index is calculated using the method of Mantua et al. (1997) as described by Lapp et al. (2012). First, the residual SSTs are calculated by subtracting the global (60^oN-60^oS) monthly SST anomalies (relative to 1961-1990) from the SST anomalies over the north Pacific region (20^oN-60^oN, 120^oE-90^oW). The Empirical Orthogonal Function (EOF) analysis is performed for these residuals and the first principal component is taken as the PDO index. The PDO index calculated from Mann-ReconMod will be referred to as PDO-Mann. Another PDO reconstruction by Shen et al. (2006) over the period AD 1600-1990 is used in this study (hereafter, PDO-Shen). This PDO reconstruction is based on proxy reconstruction of summer rainfall of eastern China extracted from historical documentary records over the period AD 1470-2000 (Shen et al. 2006). In the present study the PDO-Shen is preferred over the PDO reconstruction by McDonald et al. (2005) because PDO-Shen shows better correlation (0.67) with ERSSTv4 than the PDO reconstruction by MacDonald (0.26) over the period AD 1854-1999. All the PDO indices used in this study are shown in Fig. 1b.

2.2.4. Niño3 Index

The model evaluation for AMO, PDO, and Niño3 was performed by Malik et al. (2017) which showed that the model has reasonable skill for simulating the spatiotemporal patterns and periodicities of these ocean modes of variability.

2.2.5. External Climate Forcings
The external climate forcing datasets used in the present research are Proxy for volcanic forcing such as Stratospheric Aerosol Optical Depth (StratAOD) in the visible band (Arfeuille et al. 2014), Tropospheric Aerosol Optical Depth (TropAOD) obtained from CAM3.5 simulations with a bulk aerosol model run by fixed SSTs and CMIP emission over the period AD 1850-2000 (S. Bauer, personal communication, 2011), CO₂ (Ramaswamy et al. 2001), and Total Solar Irradiance (TSI; Shapiro et al. 2011). All these external forcings are shown in Fig. 1d. Note that strong volcanic activity occurred during the minima of solar activity i.e. Maunder Minimum (AD ~1650-1710) and Dalton Minimum (AD ~1800-1840) which can mask the solar effect on climatic variables (Breitenmoser et al. 2012). Thus, for studying the influence of solar activity it is important to remove the effects of volcanic eruptions from the climatic variable being analyzed.

2.3. Methods

We suppose there is number of random walks or time series

(0)

We build integrated profiles, , for these time series as

(0)

Residuals or de-trended walks are defined by subtracting the local trend from the original integrated profile, , such that

(0)

Where, the de-trended walk for each time series will contain elements.

(0)

The covariance matrix for de-trended walks can be defined as

(0)

The correlation coefficient between time series, and can be calculated as

(0)

The correlation matrix is calculated as

(0)

Calculate the inverse of correlation matrix as

(0)

From the inverse correlation matrix, , DPCCA can be obtained as

(0)

By Kim (2015) the DPCCA can be extended to DSPCCA as

(10)

This gives the DSPCCA coefficient that ranges between -1 and +1.

For removing non-stationarities a 1^st order polynomial is fitted in each overlapping box and then DCCA and DSPCCA are calculated on inter-annual (3-yr) to centennial (100-yr) timescales without any smoothing or filtering of the data. The significance of DCCA and DSPCCA coefficients is tested using Monte Carlo simulation. We generate 5000 surrogate samples for each original time series employing the Corrected Amplitude Adjusted Fourier Transform (CAAFT) algorithm. The surrogate data generated from CAAFT algorithm retains the same auto-correlation and amplitude distribution as the original time series. A 1^st order Autoregressive (AR1) model is fitted to original time series. From this AR1 model, 5000 realizations are generated and transformed to match the amplitude distribution, cumulative density function, and linear correlations of the original time series (Kugiumtzis 2000). Some other algorithms (e.g., AAFT; and IAAFT: Iterative AAFT) for surrogate data generation also exist but here we prefer to use CAAFT as it is a more conservative approach for significance testing (Kugiumtzis 2000). The code for the CAAFT algorithm was downloaded from the MathWorks website (http://ch.mathworks.com/matlabcentral/fileexchange/4612-surrogate-data). The correlation coefficient critical values are calculated at 90% and 95% significance.

In the present research we use three ocean modes (AMO, PDO, and Niño3) and four external forcings (TSI, CO₂, TropAOD, and StratAOD). For DCCA and DSPCCA analyses four curves are plotted in corresponding figures (e.g., Fig 2a). In these figures the DCCA represents that the effects of none of the background signals (potential modulating factors) are removed (shown as black curve) whereas the DSPCCA-AllVar represents that the effects of all background signals (potential modulating factors) are removed from the variables (AMO, PDO, and Niño3) being cross-correlated with TSI/StratAOD. The blue curve shows that the effects of remaining two ocean modes, other than the ocean mode being cross-correlated, are not removed. The green curve shows that the effects of remaining three external forcings, other than the external forcing being cross-correlated, are not removed. For instance, if AMO and TSI are cross- correlated, then the blue curve (DSPCCA-PDO.Nino3(no)) indicates that the effects of remaining three external climate forcings (CO2, TropAOD and StratAOD) are removed but it could not remove the remaining two ocean modes (PDO and Niño3) from AMO. Similarly, the green curve (DSPCCA-CO2.TropAOD.StratAOD(no)) indicates that the effects of remaining two ocean modes (PDO and Niño3) are removed but could not remove the remaining three external forcings (CO2, TropAOD and StratAOD). Thus the blue curve gives us an idea that how the remaining two ocean modes together can modulate the relationship between variables subjected to cross-correlation whereas the green curve tells us how the remaining three external forcings can modulate the relationship between the variables subjected to cross-correlation. Further, in subsequent sections DCCA and DSPCCA-AllVar will be referred to as extrinsic and intrinsic relationship/correlation, respectively. Note that DSPCCA does not remove the effect of any variable from TSI and StratAOD.